List of top Mathematics Questions asked in JEE Main

$\lim\limits_{x\rightarrow0}\left(\left(\frac{1-cos^2(3x)}{cos^3(4x)}\right)\left(\frac{sin^3(4x)}{(log_e(2x+1))^5}\right)\right)$is equal to

Let the digits a, b, c be in A.P. Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive digits are in A.P. at least once. How many such numbers can be formed?

Let $\vec{u}=\hat{i}-\hat{j}-2 \hat{k}, \vec{v}=2 \hat{i}+\hat{j}-\hat{k}, \vec{v} \cdot \vec{w}=2$ and $\vec{v} \times \vec{w}=\vec{u}+\lambda \vec{v}$. Then $\vec{u} \cdot \vec{w}$ is equal to

If the domain of the function $f(x)=\frac{[x]}{1+x^2}$, where $[x]$ is greatest integer $\leq x$, is $[2,6)$, then its range is

Let y = y(x) be a solution of the differential equation (x cos x)dy +(xy sin x + y cos x – l)dx = 0, 0 < x < $\frac{π}{2}$. If$\frac{π}{3}y(\frac{π}{3})=\sqrt3$, then $| \frac{π}{6 }y“( \frac{π}{6})+2 y'( \frac{π}{6})| $ is equal to______.

Let D_k=$\begin{vmatrix} 1 & 2k & 2k-1\\ n & n^2+n+2 & n^2 \\ n & n^2+n & n^2+n+2 \end{vmatrix} $ If $∑^n_{k=1} D_k=96,$ The n is equal to

Let $a \in R$ and let $\alpha, \beta$ be the roots of the equation $x^2+60^{\frac{1}{4}} x+a=0$. If $\alpha^4+\beta^4=-30$, then the product of all possible values of $a$ is_____

Let B =$\begin{bmatrix} 1 & 3 & α \\ 1 & 2& 3 \\ α & α & 4 \end{bmatrix}$ , α>2 be the adjoint of a matrix A and |A| = 2, then [α - 2α α] B$\begin{bmatrix} α \\ -2α \\ α \end{bmatrix}$is equal to

The number of real values $\lambda$, such that the system of linear equations $2 x-3 y+5 z=9 $ $ x+3 y-z=-18 $ $ 3 x-y+\left(\lambda^2-|\lambda|\right) z=16$ has no solution, is :-

Let $S=\{\theta \in[0,2 \pi): \tan (\pi \cos \theta)+\tan (\pi \sin \theta)=0\}$ Then $\displaystyle\sum_{\theta \in s } \sin ^2\left(\theta+\frac{\pi}{4}\right)$ is equal to _______

Rank of the word PUBLIC is?

Consider a function f:N→R, satisfying
$ f(1)+2f(2)+3f(3)+⋯+xf(x)=x(x+1)f(x);x≥2 with f(1)=1.$
Then $\frac{1}{f(2022)} + \frac{1}{f(2028)}$ is equal to $

Let $S =\{1,2,3,5,7,10,11\}$ The number of non-empty subsets of $S$ that have the sum of all elements a multiple of 3 , is _____

Let $A =\left[ a _{i j}\right], a _{i j} \in Z \cap[0,4], 1 \leq i, j \leq 2$ .
The number of matrices $A$ such that the sum of all entries is a prime number $p \in(2,13)$ is _____.

Let a and b are roots of x² – 7x – 1 = 0. The value of $\frac{a^{21} + b^{21} + a^{17} + b^{17}}{a^{19} + b^{19}}$ is?

if f(x)= $\frac{(tan1\degree)x+\log_e(123)}{x\log_e(1234)-(tan1\degree)},x>0$ , then the least value of $f(f(x))+f(f(\frac{4}{x}))$is

Let $a_1, a_2, a_3, \ldots$ be an AP If $a_7=3$, the product $a_1 a_4$ is minimum and the sum of its first $n$ terms is zero, then $n !-4 a_{n(n+2)}$ is equal to :

Let $ \alpha, \beta $ be the roots of the equation $ x^2 - \sqrt{2}x + 2 = 0 $, then $ \alpha^{14} + \beta^{14} $ is equal to:

An organization awarded 48 medals in event 'A', 25 in event 'B' and 18 in event 'C'. If these medals went to total 60 men and only five men got medals in all the three events, then how many received medals in exactly two of three events?

Let f(x) = $\displaystyle\sum_{k=1}^{10} kx^k$ , x ∈ R. If 2f(2) + f(2) = 190(2)ⁿ + 1 then n is equal to____.

\[ f(x) = \log_e \left( 4x^2 + 11x + 6 \right) + \sin^{-1} \left( 4x + 3 \right) + \cos^{-1} \left( \frac{10x + 6}{3} \right) \]then $ 36|\alpha + \beta| $ is equal to:

Let $P(S)$ denote the power set of $S = \{1, 2, 3, \ldots, 10\}$. Define the relations $R_1$ and $R_2$ on $P(S)$ as $A R_1 B$ if \[(A \cap B^c) \cup (B \cap A^c) = ,\]and $A R_2 B$ if\[A \cup B^c = B \cup A^c,\]for all $A, B \in P(S)$. Then:

Let $y=f(x)=\sin ^3\left(\frac{\pi}{3}\left(\cos \left(\frac{\pi}{3 \sqrt{2}}\left(-4 x^3+5 x^2+1\right)^{\frac{3}{2}}\right)\right)\right)$ Then, at $x=1$

If $a_r$ is the coefficient of $x^{10-r}$ in the Binomial expansion of $(1+x)^{10}$, then $\displaystyle\sum_{r=1}^{10} r^3\left(\frac{a_r}{a_{r-1}}\right)^2$ is equal to

If the value of real number a> 0 for which $x^2$-5ax+1-0 and $x^2-a x-5-0$ have a common real root is $\frac{3}{\sqrt{2 \beta}}$ then $ \beta$ is equal to_______